A167938 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416

Offset

0,2

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,-253).

Formula

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 253*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

From G. C. Greubel, Sep 09 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 23*t + 275*t^16 - 253*t^17).

a(n) = 22*Sum_{j=1..15} a(n-j) - 253*a(n-16). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-23*t+275*t^16-253*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 09 2023 *)
coxG[{16, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 18 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) )); // G. C. Greubel, Sep 09 2023
(SageMath)
def A167938_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) ).list()
A167938_list(40) # G. C. Greubel, Sep 09 2023

Crossrefs

Cf. A154638, A167881, A169452, A170758.

Sequence in context: A167077 A167183 A167695 * A168701 A168749 A168797

Adjacent sequences: A167935 A167936 A167937 * A167939 A167940 A167941

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved